Anomalous Viscosity Accretion Disk Instability

As a powerful and attractive theoretical model, accretion disks (AD) are widely believed to be sources of high-energy radiation for X-ray binaries and active galactic nuclei. Since the standard thin disk model was constructed, in the early 1970s, the stability of the disk has become an important area in the theory of AD. This is because a lot of quasi-periodic variations in X-ray binaries and active galactic nuclei are believed to be related to the instabilities of the disk. Much research is done concerning the instabilities. Except the thermal mode and the viscous mode, people find two acoustic modes in AD, the O-mode (propagating outward) and the I-mode (propagating inward). The rapid growth of these unstable modes may result in the breakdown of the thin accretion disk configuration. AD are hydrodynamic disks with turbulent viscosity, so first of all we must know the anomalous turbulent viscosity. Unfortunately the turbulent viscosity is a rather difficult problem and has disturbed the astrophysicists for a long time. We know little about it, and usually we use standard α model. It was found that the I-mode was unstable in the outer disk, and sometimes turned stable in the inner disk, for the standard α model. Recently, a new model of anomalous viscosity was found by Li X. Q. & Zhang H. The magnetic fields self-generated by the transverse plasmas are modulationally unstable in the Lyapunov sense, leading to a self-similar collapse of the magnetic flux. Highly spatially intermittent flux is responsible for generating the anomalous viscosity. In this thesis, we investigate the acoustic instabilities in the inner region of AD using the new anomalous magnetic viscosity. We use the axisymmetric hydrodynamic equations with cylindrical coordinates, and obtain the equilibrium equations. In the framework of the standard linear analysis and short-wave approximation, we can obtain the linear perturbed equations. Then we get a dispersion equation by setting the determinants of the coefficients in the linear perturbed equations equal to zero. A positive imaginary part of the frequency ω means that the mode is unstable. Finally we find the I-mode is always unstable in the inner disk, due to the anomalous magnetic viscosity. And the...